1. Field of the Invention
This invention relates in general to jet nozzles and specifically to supersonic elliptic jet nozzles.
2. Description of the Related Art
In the past, nozzles with circular, i.e., axisymmetric, cross-sections were used for supersonic jet aircraft. These nozzles were designed such that they had cross-sectional areas which contracted until sonic flow of the gases was achieved at the throat of the nozzle. Then, after the throat of the nozzle, the nozzle expanded slightly until the flow achieved supersonic speed at nozzle exit. The supersonic portion of the nozzle is designed so that shock waves and thus shock noise were limited. This type of nozzle is known as a convergent-divergent nozzle.
One conventional method of designing circular nozzles was with the Inverse Method of Freidrichs. The Method of Freidrichs has been fully described in various publications, including K.O. Freidrichs, "Theoretical Studies on the Flow Through Nozzles and Related Problems," NDRC Applied Math Panel, AMP Report 82.1R, April 1944. This publication is hereby incorporated by reference.
In the Method of Freidrichs, the centerline velocity distribution is used an input parameter. Then, using the equations of the Method of Freidrichs, the streamlines are computed and the inner nozzle geometry coordinates are calculated from the boundary of the streamlines.
The Method of Freidrichs only works for fluid flow velocities up to approximately 1.2 Mach. Therefore, in nozzles which have a final Mach number which is over 1.2, the Method of Freidrichs can be used for the lower velocity portions of the nozzle, but a different design procedure must be used for the downstream, higher velocity nozzle portions.
Another conventional and quite successful way of designing circular nozzles is with the Method of Characteristics, which has been fully described in various publications, including Ascher H. Shapiro, Thermodynamics of Compressible Fluid Flow, Ronald Press (1953). This publication is hereby incorporated by reference.
The Method of Characteristics can be used for fluid velocities above 1.0 Mach, i.e., is not limited to fluid velocities below 1.2 Mach. There are quite a few different Method of Characteristics codes. In each, the nozzle is designed according to the parameter that the angle of the nozzle wall should be such that any wave incident to the surface of the nozzle wall would be a non-reflective wave. This minimizes the formation of shock waves.
All circular nozzles, even those designed by the Method of Characteristics and/or the Method of Freidrichs, still produced an undesirable amount of noise.
In the past there were attempts to design and build elliptic nozzles. However, all nozzles designed according to these procedures were convergent only. That is, the cross-sectional area of the nozzle only became smaller, thus resulting in large shock waves and noise.
Furthermore, none of the previous methods of designing elliptic nozzles translated the convergent-divergent circular nozzle geometry into elliptic coordinates.